Pass Functional Skills logo

Factors and multiples

Factors and multiples for A Level Physical Education AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Physical Education
  • Higher
  • Spec R13 · R12 · R17
  • 8 min read
  • 7 revision boxes

Introduction

2 boxes
1 min read

What is factors and multiples?

Listen to this box

Transcript

A short spoken summary of factors and multiples and where it is used.

A spoken walk-through of factors and multiples before you read the notes.
Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.
6 rows

The factors and multiples reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

3 boxes
3 steps

How to work with factors and multiples

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for factors and multiples in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: ≈160\approx 160
3 rules

Key facts: Factors and multiples

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How factors and multiples behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How factors and multiples behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How factors and multiples behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with factors and multiples

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for factors and multiples in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
3 marks · worked

Worked example: factors and multiples

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing factors and multiples laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
3 marks · worked

Practice question 7: 34×25\frac{3}{4} \times \frac{2}{5}

Work through the method one line at a time and write down what changes at each step.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
9,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is factors and multiples usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Physical Education AQA Higher paper?
Yes — it sits in the Algebra strand.